The role of Bessel processes on the sequential test for a unit root in autoregressive process and criticality in branching processes

摘要

We consider sequential testing problems on singularity in stochastic processes. Especially we focus on unit root test in autoregressive process and criticality test in branching process. Using diffusion approximation and time change, Bessel processes and Bessel bridges on squared Bessel play crucial roles to analyze the operating characteristics such as size, powers, moments of the sequential test statistics and the stopping times.